Optical shape sensing system and method

ABSTRACT

The present invention relates to an optical shape sensing system, comprising an optical fiber sensor comprising an optical fiber having embedded therein a number of at least four fiber cores ( 1  to  6 ) arranged spaced apart from a longitudinal center axis ( 0 ) of the optical fiber, the fiber cores each having a resonance wavelength in response to light introduced into the fiber cores ( 1  to  6 ) in an unstrained state thereof. The system further comprises an optical interrogation unit ( 21 ) configured to interrogate the fiber cores ( 1  to  6 ) with light in a scan wavelength range including the resonance wavelengths of the fiber cores in an unstrained state of the fiber cores ( 1  to  6 ). The scan wavelength range is set such that a center wavelength of the scan wavelength range is decentered with respect to the resonance wavelength of at least one of the fiber cores ( 1  to  6 ).

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the U.S. National Phase application under 35 U.S.C.§ 371 of International Application No. PCT/EP2019/074880 filed Sep. 17,2019, which claims the benefit of European Patent Application Number18195663.2 filed Sep. 20, 2018. These applications are herebyincorporated by reference herein.

FIELD OF THE INVENTION

The present invention generally relates to the field of optical shapesensing. In particular, the present invention relates to an opticalshape sensing system, comprising an optical fiber sensor comprising anoptical fiber having embedded therein at least four outer fiber cores.Furthermore, the invention relates to an optical shape sensing method.

BACKGROUND OF THE INVENTION

Optical shape sensing (OSS) is a technology with which thethree-dimensional shape of a special optical fiber can be reconstructedfrom the reflections of light within the fiber. This technology enables,for example, real-time 3D visualization of the full shape of deviceslike medical devices, for example catheters and guidewires. The shapesof the medical devices can be overlaid on X-ray images or apre-operative CT scan. In this way, a physician can navigate the devicesduring a procedure without the need of X-ray tracking.

In optical shape sensing, an optical fiber sensor, also referred to asoptical shape sensing fiber, is interrogated with light coupled into thefiber cores of the fiber, and distributed strain and temperature signalsare obtained from back-scattered spectra obtained with an interrogatorunit incorporating interferometers. A standard optical fiber sensor hasthree outer fiber cores (in the present description, fiber coresarranged spaced apart from the center axis of the fiber are also denotedas outer fiber cores) helically wound around a fourth core, which isarranged in the radial center of the fiber. The responses of the fibercores to strain and temperature are measured as phase differences of theoptical signals from the interferometers, as a function of delayposition along the fiber sensor. The phase differences are obtained withrespect to a reference measurement in which the fiber sensor is in awell-defined shape, for example a completely straight shape. From thephase differences of the fiber cores, the strain and temperaturedifferences can be deduced for each fiber core. The strain signals willbe the sum of bend strain in two orthogonal directions, as well as twiststrain and axial strain, the latter being the strain in the longitudinaldirection of the optical fiber sensor. From these four positiondependent quantities, the shape of the fiber sensor can bereconstructed. For high-accuracy shape sensing, accurate fiber sensorproperties are needed in the shape reconstruction model. Theseproperties can be determined for each individual optical fiber in acalibration process.

A further extension of the shape sensing technology is to be able todistinguish the effect of temperature from the effect of axial strain.In order to do so at least one additional core with a differenttemperature sensitivity is needed, as, for example, described in WO2016/099976 A1.

As described above, the shape of the optical sensing fiber is calculatedfrom the position dependent strain signals measured for several,typically four cores inside the fiber. For example, bending the fiber inthe plane defined by a fiber core and the fiber center will result in astrain on that fiber core if that core is not arranged in the center ofthe fiber. In this case, the strain 8 is the quotient of the distance aof that core from the center axis of the fiber and the radius r of thebend of that core. The bend strain is measured here relative to thestraight and unstrained state of the fiber. The magnitude of the straincan be deduced from the amount of spectral shift of the reflected light.In the case that the fiber cores contain Fiber Bragg Gratings (FBGs),due to the periodic nature of the Bragg gratings, the sensor willreflect the light of one particular wavelength, called the resonancewavelength. In case the fiber core is elongated (positively strained)relative to the reference measurement, the periodicity of the FBGs willincrease, resulting in an increase in resonance wavelength. On the otherhand, in case of compressive (negative) strain, the periodicity of theFBGs will decrease, resulting in a decrease in resonance wavelength. Thelower the radius of curvature of the bend, the larger the shift δλ inresonance wavelength (in either positive or negative direction,depending on the location of the fiber core in the bend):

$\begin{matrix}{{\delta\lambda} = {{\lambda_{o}{\xi\varepsilon}} = {\frac{\lambda_{o}\xi\alpha}{r}{\sin\left( {{\vartheta_{twist}(z)} + \varphi} \right)}}}} & (1)\end{matrix}$wherein λ₀ is the resonance wavelength of the fiber cores, moreprecisely the FBGs, in the unstrained state, and ξ is a strain-opticnumber (≈0.8) that accounts for the strain-induced change of refractiveindex, which affects the relation between Bragg period and wavelength.The sine function describes the varying location of the outer core as itis helically twisted around the fiber center.

_(twist) is the cumulative twist angle of the core, which is the sum ofthe intrinsically present twist in the spun fiber and the externallyapplied twist. φ is an offset angle which is related to the orientationof the bend plane and the angle of the fiber core at a referenceposition. For reasons of clarity, in equation (1) only strain due tobend is assumed.

When an optical fiber sensor is inserted, for example, in a lumen of amedical device, it will experience a varying radius of curvature. Themedical device may be pre-shaped and during handling of the device itwill change its form. The smallest radius of curvature encountered bythe optical fiber sensor depends on the design of the device, theoptical fiber itself and the environment that it is being used in. Forexample, the vasculature of a human can, for example, be very tortuous.To be able to access these kind of vessels, more flexible devices willbe used. An optical fiber sensor inside such medical devices should beable to withstand small radii of curvature. However, there is a limit,which is related to the minimum measurable bend radius of the opticalfiber sensor.

In shape sensing, typically a spectrum is recorded for each fiber coreby scanning a light source over a fixed wavelength range Δλ centered onthe resonance wavelength of the FBGs in the unstrained situation. Theminimum bend radius that has a resonance still inside the measuredspectrum is:

$\begin{matrix}{r_{\min} = \frac{2\lambda_{0}\xi a}{\Delta\lambda}} & (2)\end{matrix}$

For a scan range of Δλ=17 nm centered around λ₀=1545 nm, ξ=0.8, and a=35μm, the minimum measurable bend radius will be 5.1 mm. If the opticalfiber sensor is bent to lower curvatures, no signal will be measured fora fiber core that is in the bend plane.

It appears from equation (2) that the minimum measurable bend radius canbe reduced by reducing the fiber core distance a and/or by increasingthe scan wavelength range Δλ. Reducing the outer fiber core distance ahas the disadvantage that it reduces the sensitivity to bend strain andalso the sensitivity to twist strain, as the sensitivity to twist strainscales with a². The required accuracy on the twist is high, thereforereducing the outer fiber core distance from the center axis of the fiberis not favorable. Increasing the scan range Δλ is disadvantageous forother reasons. It decreases the signal to noise ratio, because theresonance peak fills the spectrum relative less. Further, the delaylength between two consecutive nodes (data points as a function ofposition on the fiber) is decreased, giving an increase of data pointsfor the same physical length of the fiber.

WO 2018/075911 A1 proposes to provide an optical fiber sensor with morethan three outer fiber cores, wherein the fiber cores are arranged atmultiple different radial distances from the center axis of the fiber.For small bend radii to be measured one has to switch to the fiber coresat lower distance which can lead to lower accuracy of the shape sensingmeasurement. Such a design of an optical fiber sensor thus suffers froma loss of accuracy.

US 2016/047976 A1 discloses a fibre-optic sensor comprising an opticalwaveguide having at least one first core and a cladding surrounding thefirst core, wherein the first core extends substantially over the entirelength of the optical waveguide, wherein the sensor has at least onesecond core which is at least partly surrounded by the cladding, whereinthe longitudinal extent of the second core is less than the total lengthof the optical waveguide and at least one Bragg grating is introducedinto the second core.

US 2007/297712 A1 discloses an optical fiber sensor for detectingcurvature of a body/structure. The sensor comprises a cladding having anouter periphery. A central core receives and transmits light. Thecentral core has Bragg gratings and is positioned in neutral planes ofthe cladding.

David Berra et al. “Multipoint Two-Dimensional Curvature Optical FiberSensor Based on a Nontwisted Hohogeneous Four-Core Fiber” discloses amultipoint two-dimensional curvature optical fiber sensor based on anontwisted homogeneous four-core fiber.

U.S. Pat. No. 7,324,714 B1 discloses an apparatus which includes amulticore fiber including three cores, wherein the three cores includetwo pairs of cores, each pair of cores lying in a plane. The planes ofthe two pairs of cores are non-coplanar. The multicore fiber includes arosette, the rosette including three coplanar interferometers, whereineach interferometer is located in a respective core of the three cores.

US 2018/195856 A1 discloses an optical fiber which includes primaryoptical cores having a first set of properties and secondary opticalcores having a second set of properties. The primary set of propertiesinclude a first temperature responce, and the secondary set ofproperties include a second temperature response sufficiently differentfrom the first temperature response to allow a sensing apparatus whencoupled to the optical fiber to distinguish between temperature andstrain on the optical fiber.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an optical shapesensing system allowing for improved shape sensing measurements.

It is a further object of the present invention to provide an opticalshape sensing method allowing for improved shape sensing measurements.

According to a first aspect of the invention, an optical shape sensingsystem is provided, comprising

an optical fiber sensor comprising an optical fiber having embeddedtherein a number of at least four fiber cores arranged spaced apart froma longitudinal center axis (0) of the optical fiber, the fiber coreseach having a resonance wavelength in response to light introduced intothe fiber cores in an unstrained state thereof,

an optical interrogation unit configured to interrogate the fiber coreswith light in a scan wavelength range including the resonancewavelengths of the fiber cores in an unstrained state of the fibercores,

wherein the optical interrogation unit is configured to set the scanwavelength range such that a center wavelength of the scan wavelengthrange is decentered with respect to the resonance wavelength of at leastone of the fiber cores.

The optical shape sensing system according to the present inventionallows for measuring smaller bend radii by firstly providing aredundancy in the number of fiber cores over the standard fiber sensorhaving three outer cores only, and secondly by setting the centerwavelength of the scan wavelength range decentered with the resonancewavelength of at least one, e.g. some or all, of the fiber cores. Theresonance wavelengths of the fiber cores may be provided by one or morewavelength dependent reflective structures, which preferentially arefiber Bragg gratings, along the length of the respective fiber core. Bydecentering the center wavelength of the scan wavelength range withrespect to one or more of the fiber cores, the scan wavelength rangebecomes asymmetrical with respect to the resonance wavelength of the oneor more of the fiber cores. An asymmetrical scan wavelength range withrespect to the resonance wavelength of one or more outer fiber coresallows for measuring smaller bend radii of the fiber sensor withoutincreasing the scan wavelength range and/or without reducing thedistance of the outer fiber cores from the center axis of the fiber, aswill be further explained herein.

The optical interrogation unit may be configured to set the scanwavelength range such that the center wavelength of the scan wavelengthrange is decentered with respect to the resonance wavelengths of allfiber cores. This embodiment provides an asymmetry of the scanwavelength with respect to all fiber cores.

The number of fiber cores may, in combination with or alternative to theaforementioned or subsequent embodiments, comprise a first subset offirst fiber cores having a first resonance wavelength in response tolight introduced into the first fiber cores in an unstrained statethereof, and a second subset of at least one second fiber core having asecond resonance wavelength in response to light introduced into the atleast one second fiber core in an unstrained state thereof, wherein thefirst resonance wavelengths differ from the second resonance wavelength.The first resonance wavelengths may be equal with respect one another,and the second resonance wavelengths may be equal to one another whichsimplifies, inter alia, manufacturing of the fiber sensor.

In connection with the previous embodiment, the interrogation unit maybe configured to set the center wavelength of the scan wavelength rangesuch that the center wavelength of the scan wavelength range isdecentered with respect to the first resonance wavelengths and centeredon the second resonance wavelength or vice versa.

In this embodiment, an asymmetry of the scan wavelength range isprovided for one of the subsets of fiber cores, while the scanwavelength range is symmetrical with respect to the other subset.

Alternatively, the interrogation unit may configured to set the scanwavelength range such that the center wavelength is between the firstand second resonance wavelengths. Further, the center wavelength may beset in the middle between the first and second resonance wavelengths. Inthe latter embodiment, the center wavelength has an equal wavelengthoffset with respect to both, the first and second resonance wavelengths.

The resonance wavelengths of all fiber cores may be equal. Thisembodiment further simplifies the manufacturing of the fiber sensor. Inthis embodiment, the center wavelength of the scan wavelength range isdecentered with respect to all fiber cores.

The scan wavelength range may be set such that the center wavelength isdecentered with respect to the resonance wavelengths of at least onefiber core by less than half the scan wavelength range. The offset maybe less than a third, further less than a quarter of half the scanwavelength range.

The fiber cores of the fiber sensor may be distributed in azimuthaldirection around the center axis equidistantly with respect to oneanother.

Alternatively, the fiber cores may be distributed in azimuthal directionaround the center axis non-equidistantly with respect to one another.

The number of fiber cores arranged at a radial distance from thelongitudinal center axis is 5, 6, or more.

The fiber cores may have an equal distance from the center axis.

The optical optical fiber may further comprise a central fiber corearranged on the center axis of the fiber.

The optical shape sensing system may further comprise an evaluation unitconfigured to reconstruct the shape of the fiber sensor using thereflection spectra received from the fiber cores.

The outer fiber cores may be helically wound around the center axis ofthe fiber sensor.

According to a second aspect, an optical shape sensing method isprovided, comprising

providing an optical fiber sensor comprising an optical fiber havingembedded therein a number of at least four fiber cores arranged spacedapart from a longitudinal center axis of the optical fiber, the fibercores each having a resonance wavelength in response to light introducedinto the fiber cores in an unstrained state thereof,

interrogating the fiber cores with light in a scan wavelength rangeincluding the resonance wavelengths of the fiber cores in an unstrainedstate of the fiber cores,

the interrogating comprising setting the scan wavelength range such thata center wavelength of the scan wavelength range is decentered withrespect to the resonance wavelength of at least one of the fiber cores.

The optical shape sensing method according to the invention has the sameor similar advantages and embodiments as described above with respect tothe system.

According to a third aspect, a computer program is provided comprisingprogram code means for causing a computer to carry out the steps of themethod according to the second aspect when said computer program iscarried out on a computer.

It is to be understood, that all embodiments described above can becombined with one another in order to provide an optical shape sensingsystem and an optical shape sensing method, allowing for measuring bendradii of the optical fiber sensor as small as possible.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will be apparent from andelucidated with reference to the embodiments described hereinafter. Inthe following drawings

FIG. 1 shows a block diagram illustrating an example of an optical shapesensing system;

FIG. 2 shows a perspective view of an example of a standard opticalfiber sensor;

FIG. 3A shows a cross-section of a standard optical fiber sensor;

FIG. 3B shows a diagram of simulation results for the optical fibersensor in FIG. 3A, wherein the difference in resonance wavelength andcenter wavelength of a scan wavelength range is plotted as a function ofposition on the optical fiber sensor having a bend;

FIG. 4A shows an embodiment of an optical fiber sensor, which has sixouter cores;

FIG. 4B shows a diagram of simulation results for the optical fibersensor in FIG. 4A, wherein the difference in resonance wavelength andcenter wavelength of a scan wavelength range is plotted as a function ofposition on the optical fiber sensor;

FIG. 5A shows an embodiment of an optical fiber sensor, which has sixouter cores;

FIG. 5B shows a diagram of simulation results for the optical fibersensor in FIG. 5A, wherein the difference in resonance wavelength andcenter wavelength of a scan wavelength range is plotted as a function ofposition on the optical fiber sensor;

FIG. 6A shows an embodiment of an optical fiber sensor, having six outercores similar to FIG. 4A;

FIG. 6B shows a diagram of simulation results for the optical fibersensor in FIG. 6A, wherein the difference in resonance wavelength andcenter wavelength of a scan wavelength range is plotted as a function ofposition on the optical fiber sensor;

FIG. 7A shows an embodiment of an optical fiber sensor, which has sixouter cores similar to FIG. 4A;

FIG. 7B shows a diagram of simulation results for the optical fibersensor in FIG. 7A, wherein the difference in resonance wavelength andcenter wavelength of a scan wavelength range is plotted as a function ofposition on the optical fiber sensor;

FIG. 8A shows the optical fiber sensor in FIG. 7A;

FIG. 8B shows a diagram of simulation results for the optical fibersensor in FIG. 8A, wherein the difference in resonance wavelength andcenter wavelength of a scan wavelength range is plotted as a function ofposition on the optical fiber sensor;

FIGS. 9A and 9B show diagrams of simulation results for a gain factorf=r_(min)/r₀ and for r₀/r_(x) as function of a decentering of a centerwavelength of a scan wavelength range with respect to resonancewavelengths of two sets of outer cores; and

FIG. 10 shows a diagram of simulation results for the smallest radius ofcurvature measurable with six outer cores as function of the smallestradius still measurable with four cores for various optical fiber sensordesigns.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 schematically shows parts of an optical fiber sensor system 10configured as a multi-channel optical frequency domain reflectometry(OFDR)-based and distributed-strain sensing system for sensing anoptical fiber sensor 12. The optical fiber sensor 12 comprises anoptical fiber having embedded therein a plurality of fiber cores 14, 16,18, 20, in the present example four cores with one center core 16 andthree outer cores 14, 18, 20. The optical fiber sensor shown in FIG. 1is a standard fiber sensor. It is to be noted here that the presentinvention proposes optical fiber sensor designs having more than threeouter cores. FIG. 2 shows a piece of length of the fiber cores 14, 16,18, 20 with the outer cores 14, 18 20 spiraled around the center core16. The center core 16 is arranged on the center axis of the opticalfiber sensor 12. The outer fiber cores 14, 18, 20 are angularly spacedwith respect to one another in azimuthal direction around thelongitudinal center axis of the optical fiber sensor 12. Thelongitudinal center axis coincides with the center core 16. According toa number of four cores in the present example, the angular spacingbetween neighboring outer cores may be 120°.

With reference again to FIG. 1 , the optical shape sensing system 10comprises an interrogator unit 21. The interrogator unit 21 may comprisea tuneable light source 22 which can be swept through a range of opticalfrequencies, also referred to as scan wavelength range. The lightemitted by the light source 22 is coupled into an opticalinterferometric network 24 having optical channels 24 a, 24 b, 24 c, 24d according to the number of fiber cores 14, 16, 18, 20 of optical fibersensor 12. In case the optical fiber sensor 12 has more than four cores,the optical interferometric network 24 may have a corresponding numberof optical channels.

When the tuneable light source 22 is swept through a range of opticalfrequencies, each channel 24 a, 24 b, 24 c, 24 d and thus each fibercore 14, 16, 18, 20 of the optical fiber sensor 12 is simultaneously andindependently optically interrogated, and the interferometric signalsbased on the reflection spectrum returning from each of the fiber cores14, 16, 18, 20 are routed to a processing unit or data acquisition unit26 via respective photodetectors 25. The distributed strain measurementsfrom the cores 14, 16, 18, 20 using the multiple channel OFDR system maythen be exported for further processing to an evaluation unit 27, inparticular for three-dimensional shape reconstruction of the opticalfiber sensor 12 and for visual display of the reconstructedthree-dimensional optical fiber sensor 12.

In embodiments of the optical fiber sensor 12, the fiber cores 14, 16,18, 20 may have Fiber Bragg Gratings (FBGs) formed by periodicvariations in the refractive index. For the sake of simplicity, FBGshaving a single resonance wavelength are considered herein. An FBGreflects light of a certain wavelength (resonance wavelength) thatdepends on the grating period of the FBG, and transmits all otherwavelengths. Due to a bend of the optical fiber sensor 12, the gratingperiod is affected by a strain, and measurement of the reflectedwavelength for any position along the fiber allows determining the localstrain. The optical fiber sensors 12′ according to embodiments of thepresent invention described below, may also comprise such FBGs.

Optical interrogation of the optical fiber sensor 12 gives theinformation needed to, in principle, reconstruct the three-dimensionalshape of the whole fiber sensor in real time. Given an appropriatereference frame, it is possible to know the exact orientation andposition of the complete fiber sensor 12 in real time.

When an optical fiber sensor, like the optical fiber sensor 12, is used,for example in a medical device like a catheter or guidewire, the devicewill change its form during handling of the device. For example, if thedevice is a catheter for introducing into the vasculature of a human,which can be very tortuous, the device and, thus, the optical fibersensor 12 will experience bends along its length which may have radii ofcurvature which can be very small. However, in optical shape sensingtechnology, there is a limit which is related to the minimum measurablebend radius of the optical fiber sensor.

Referring to equation (2) above, the minimum measurable bend radius ofthe standard optical fiber sensor 12 will be 5.1 mm for a scan range ofΔλ=17 nm centered around the resonance wavelength λ₀=1545 nm of thefiber cores in an unstrained state, ξ=0.8, and a=35 μm (as to thedefinition of these parameters, see above). If the standard opticalfiber sensor 12 is bent to lower curvatures, i.e. to curvatures with abend radius below 5.1 mm, no signal will be measured for a fiber corethat is in the bend plane.

FIG. 3A shows a cross-section of the standard optical fiber sensor 12,wherein the three outer cores are labelled with 1, 2, 3, and the centralcore is labelled with 0. FIG. 3B shows simulation results (see equation(1)) for the optical fiber sensor 12, with a bend having a radius of 5.1mm. In FIG. 3B, the difference in λ_(res), i.e. the resonance wavelengthfor each of the fiber cores 1, 2, 3 in the bent state, and λ_(c) i.e.the center wavelength of the scan wavelength range is plotted asfunction of position on the optical fiber sensor along its length, forthe three outer cores 1, 2, 3 separated by 120° in azimuthal directionaround the center axis (central core 0). The spectrum of the center core0 is not depicted in FIG. 3B, as there will be no shift in resonancewavelength due to bend strain for the central core 0. The twist rate ofthe outer fiber cores 1, 2, 3 is 50 turns per meter and 1 indexcorresponds to 48.2 μm. The grey-shaded area gives the scan wavelengthrange needed to cover the shift in resonance wavelength of the outercores due to the bend. In FIG. 3B, curve 41 shows a simulation resultfor core 1, curve 42 shows the simulation result for core 2, and curve43 shows the simulation result for core 3. The minimum scan range neededto always cover the 5.1 mm bend radius (which is, for all orientationsof the optical fiber sensor with respect to the bend) is shown in FIG.3B by dotted lines 51, 52 at λ_(res)−λ_(c)=±8.4 nm.

FIG. 4A shows an embodiment of an optical fiber sensor 12′ according tothe invention, which comprises a number of outer fiber cores which islarger than 3. In other words, the optical fiber sensor 12′ provides aredundancy by adding further outer fiber cores which provides aredundancy in a shape sensing measurement of the fiber 12′ to allow formeasuring smaller bend radii of the fiber 12′ than with the three outerfiber cores of the standard sensor 12. In FIG. 4A, the outer fiber coresare labelled with reference numerals 1 to 6. The fiber sensor 12′ alsoincludes a center core 0, wherein 0 also denotes the center axis of thefiber sensor 12′. So there are three outer fiber cores of a first subsetof fiber cores, for example fiber cores 1, 3, 5, and three outer fibercores of a second subset of fiber cores, for example fiber cores 2, 4, 6(it is to be noted that the allocation of the fibers to the first subsetand the second subset is not critical).

As shown in FIG. 4A, the fiber cores 1, 3, 5 of the first subset and thefiber cores 2, 4, 6 of the second subset may have the same radialdistance from the center axis (center core 0). Further, the fiber cores1 to 6 may be arranged equidistantly around the center axis in azimuthaldirection. The angle between two neighboring fiber cores of the fibercores 1 to 6 thus is 60°. The fiber cores 1,3, 5 may have a first singleresonance wavelength in an unstrained state of the fiber 12′, and thefiber cores 2, 4, 6 may have second single resonance wavelength in anunstrained state of the fiber sensor 12′. In this example, the first andsecond resonance wavelengths are qual.

The fiber cores of the second subset of fiber cores may be helicallywound around the center axis of the sensor 12′.

To be able to distinguish the four position-dependent quantities neededfor shape reconstruction with the optical fiber sensor 12′, whichquantities are bend strain in two orthogonal directions, twist and axialstrain, the signals of the central core 0 and at least three of theouter cores 1 to 6 should be known.

FIG. 4B shows the simulation results for the optical fiber sensor 12′ inFIG. 4A where again the difference in resonance wavelength λ_(res) andcenter wavelength λ_(c) of the scan wavelength range is plotted as afunction of position on the optical fiber sensor 12′, as described withrespect to FIG. 3B. The grey-shaded area gives the scan wavelength rangeneeded to include the resonances of at least three of the outer cores 1to 6. In FIG. 4B, curves 41 to 46 show the simulation results for theouter fiber cores 1 to 6 (the result for the center core 0 is againomitted in FIG. 4B). As can be seen from the diagram in FIG. 4B, theblack-dotted lines 51 and 52 are not at the maxima of the fiber coresignals any more, which means that with the same scan wavelength range(±8.4 nm) a smaller bend radius can be measured. In the present case, aminimum bend radius r_(min) of 4.5 mm can be measured. Comparing thesimulation results of FIGS. 3B and 4B, it reveals that the redundancy infiber cores by providing, for example, six outer fiber cores instead ofthree, the minimum measurable bend radius can be reduced withoutincreasing the scan wavelength range and without decreasing the distanceof the outer cores from the center axis.

In order to have a measure for the beneficial effect of redundancy inouter fiber cores in comparison with a standard optical fiber sensorhaving three outer cores, like optical fiber sensor 12 in FIG. 3A, again factor f may be calculated that is obtained by the redundancy dueto the amount n of cores without increasing the scan wavelength range:

$\begin{matrix}{{f = {\cos\left( {\frac{\pi}{n - 1}{floor}\left( {\frac{n}{2} - 2} \right)} \right)}},{{{for}n} \geq 4}} & (3)\end{matrix}$where n is the total number of fiber cores (including the center coreand n−1 outer fiber cores). For n=4 (standard optical fiber sensor), fis 1. For n=7 (six outer cores and one center core), f is about 0.87.This means that for a symmetrical arrangement of six outer cores (60°angle between two neighboring outer cores), the minimum measurable bendradius can be reduced by a factor of 0.87, i.e. from 5.1 mm to 4.5 mm,with the same scan wavelength range.

The gain factor f and, thus, the minimum measurable band radius, can befurther reduced by one or more of the following measures which will bedescribed in connection with further embodiments.

In general, optimization of the gain factor f can be done by changingthe fiber core angles with respect to one another, and/or by changingthe core optical properties, and/or by introducing an asymmetry betweenthe scan wavelength range and the resonance wavelength of the fibercores in the unstrained state thereof. These measures will be describedhereinafter.

FIG. 5A shows an embodiment of an optical fiber sensor 12′ having sixouter cores 1 to 6 wherein the difference to the embodiment in FIG. 4Ais that the fiber cores 1 to 6 in FIG. 5A are not equidistantlydistributed in azimuthal direction around the center core 0 extendingalong the central axis of the fiber 12′. In the embodiment in FIG. 5A,the angle between some of neighboring fiber cores, for example fibercores 2 and 3, is smaller than the angle between other neighboring fibercores, for example fiber cores 1 and 2. For example, the smaller anglebetween fiber cores 2 and 3, 4 and 5, and 6 and 1 may be 30°, while thelarger angle between fiber cores 1 and 2, 3 and 4, and 5 and 6 is 90°.It should be noted that the number of six outer fiber cores as shown inFIG. 5A is exemplary, and any other number of outer fiber cores can betaken as well, as long there is redundancy. In the embodiment in FIG.5A, a first subset of outer cores 1, 3, 5 are placed at 0°, 120° and240°, and a second subset of three cores 2, 4, 6 having the samerelative angles between them are placed under an angle of θ=30° withrespect to the fiber cores 1, 3, 5 of the first subset. For a 7-coreoptical fiber sensor (six outer fiber cores and one center core) witharbitrary θ, the gain factor f is given by:

$\begin{matrix}{{f = {\max\left\{ {{\cos\left( \frac{{❘\theta ❘} - {2{\pi/3}}}{2} \right)},{- {\sin\left( \frac{{❘\theta ❘} - {2{\pi/3}}}{2} \right)}}} \right\}}},{{{for} - \frac{\pi}{3}} < \theta \leq {\pi/3}}} & (4)\end{matrix}$

The lowest gain factor f is obtained for θ=30° (f=0.71) in the 7-corefiber sensor 12′. FIG. 5B shows a diagram similar to FIG. 4B ofsimulation results for the six outer cores 1 to 6 in FIG. 5A. Thegrey-shaded area again gives the scan wavelength range needed to includethe resonances of at least three outer cores, and the dotted lines 51,52 depict the minimum scan wavelength range needed to cover theresonances of all fiber cores for the 5.1 mm bend radius.

Thus, with an angle θ=30°, a reduction in minimum measurable bend radiusto 3.6 min can be achieved, which is lower than in the more symmetriccase of the embodiment in FIG. 4A with θ=60°, for the same fixed scanwavelength range of ±8.4 nm.

A further measure to optimize the minimum measurable bend radius of anoptical fiber sensor is to properly choose the optical properties of thefiber cores in the first and the second subset. Such an optical propertywhich may be varied among the fiber cores may be the resonancewavelength λ₀ of the fiber cores in an unstrained state thereof. FIG. 6Ashows an embodiment of an optical fiber sensor 12′, which isgeometrically identical with the embodiment in FIG. 4A, comprising afirst subset of fiber cores, for example fiber cores 1, 3, 5 and asecond subset of fiber cores, for example fiber cores 2, 4, 6. Thedifference to the embodiment in FIG. 4A is that the resonancewavelengths λ_(0A) of the first subset of outer cores in an unstrainedstate thereof is different from the resonance wavelengths λ_(0B) of thefiber cores of the second subset of fiber cores in an unstrained statethereof. The resonance wavelengths of the fiber cores of the firstsubset may be decentered from the center wavelength λ_(C) of the scanwavelength range, while the resonance wavelengths of the fiber cores ofthe second subset is kept at the scan wavelength range center λ_(C). Asan example, for the first subset of fiber cores, λ_(0A)−λ_(C) may be 4.3nm, while for the second subset of outer fiber cores λ_(0B)=λ_(C). It isalso conceivable that λ_(0A,0B)−λ_(C) deviates from zero for the firstsubset of three outer fiber cores as well as for the second subset ofthree outer fiber cores. FIG. 6B shows simulation results for theoptical fiber sensor 12′ in FIG. 6A, wherein the difference in resonancewavelength λ_(res) in the strained state and the center wavelength λ_(C)of the scan wavelength range is plotted as function of position on thesensor for the outer fiber cores 1-6, as explained with respect to FIG.3B.

It is also conceivable to combine the embodiment in FIG. 6A with theembodiment in FIG. 5A, i.e. to change the angle positions of the outerfiber cores 1 to 6 in a non-equidistant manner as shown in FIG. 5A.

A further option in combination with the redundancy of outer opticalfiber cores in order to reduce the minimum measurable bend radius is tointroduce an asymmetry between the resonance wavelengths, for example ofthe FBGs of the unstrained fiber cores, and the center wavelength of thescan wavelength range that is used to interrogate the fiber cores. Thismeans λ₀≠λ_(C), even in case λ₀ is the same for all fiber cores. To thisend, the interrogation unit 21 of the optical shape sensing system 10 inFIG. 1 is configured to set the center wavelength λ_(C) such that thecenter wavelength differs from the resonance wavelengths of one or moreof the fiber cores 1 to 6. FIG. 7A and FIG. 8A show in each case across-section of an optical fiber sensor 12′ having six outer fibercores 1 to 6 and one center core 0 in each case. The geometrical designsof the optical sensing fiber 12′ in FIG. 7A and in FIG. 8A are the samewith respect to one another. In the embodiment of FIG. 7A, the scanwavelength range is set such that the resonance wavelength λ₀ of theunstrained fiber cores 1 to 6 is completely at the edge of the scanrange, i.e. λ₀−λ_(C)=8.4 nm in this example. In this case, the minimummeasurable bend radius becomes as low as 2.6 mm for a 16.7 nm scanrange. This configuration however means that the resonances are only inthe scan wavelength range in case of the limit of a completely straightfiber. If one defines the minimum radius of curvature for which allfiber cores 1 to 6 are still in the measured spectrum with r_(x), thenr_(x)=∞ in this case. This may be an undesirable situation, as theredundancy in fiber cores cannot be used for anything else any more, noteven in cases of lower curvature. Lowering the decentering λ₀−A_(c) willlower r_(x) as well. FIG. 8A and FIG. 8B give an example, in which atrade-off is made between r_(min) which is the smallest radius stillmeasurable with four fiber cores (including the center core) and r_(x).For example, if λ₀−λ_(C)=2.3 nm for all outer fiber cores 1 to 6,r_(min)=3.5 mm and r_(x)=7.0 mm.

In the following table 1, the simulation results of the standard case inFIG. 3A and the embodiments in FIGS. 4A, 5A, 6A, 7A and 8A aresummarized. In table 1, the gain factor f, r_(min) (the smallest radiusof curvature still measurable with four fiber cores including the centercore) and r_(x) (the minimum radius of curvature for which all fibercores are still in the measured spectrum) are listed.

TABLE 1 16.7 4 120° between outer cores 3A 1 5.1 5.1 16.7 7 60° betweenouter cores 4A 0.87 4.5 5.1 16.7 7 Core angles: 0°, 30°, 120°, 150°, 5A0.71 3.6 5.1 240° and 270° 16.7 7 λ₀ − λ_(c) is 4.3, 0, 4.3, 0, 4.3 and0 nm 6A 0.66 3.4 10.6  16.7 7 λ₀ − λ_(c) is 2.8, −2.8, 2.8, −2.8, 2.8 —0.75 3.9 7.8 and −2.8 nm 16.7 7 λ₀ − λ_(c) is 8.4 nm for all cores 7A0.50 2.6 ∞ 16.7 7 λ₀ − λ_(c) is 2.3 nm for all cores 8A 0.68 3.5 7.0

Table 1 also includes an embodiment in line 5 of table 1, in whichλ₀−λ_(C) deviates from zero for the outer fiber cores of the firstsubset as well as for the outer fiber cores of the second subset asmentioned above, wherein λ₀−λ_(C)=2.8 nm for the outer fiber cores ofthe first subset and λ₀−λ_(C)=−2.8 nm for the outer fiber cores of thesecond subset.

The above described measures of optimizing the design of the opticalfiber sensor 12′ and optimizing the interrogator unit 21 (FIG. 1 ) whichprovides the scan range of interrogation of the fiber cores of theoptical fiber sensor 12′ can all be combined for an application to beperformed.

For example, the resonance wavelength λ₀ in the unstrained state of thefiber cores may deviate from fiber core to fiber core due to some otherdesign constraint. For example, in case it is desired to distinguishtemperature from axial strain, at least one fiber core with atemperature sensitivity different from the other cores has to be used.This can result in a deviating λ₀ for this fiber core. For the case of a7-fiber core shape sensing fiber with a design similar to the one inFIG. 6A, some options will be described in the following. To this end,it is defined Δ=λ_(0,A)−λ_(0,B), where A and B denote the two subsets ofthree outer cores separated by 60°. It is now possible to calculater_(min) and r_(x) for a certain Δ and λ_(0,A)−λ_(C). The results aregiven in FIGS. 9A and 9B and in FIG. 10 .

In FIG. 10 , 1/r_(x) is plotted as a function of r_(min) for a pluralityof Δ in the range from Δ=0.0 nm up to Δ=±12.0 nm. FIG. 9A showssimulation results for the gain factor f=r_(min)/r₀, and FIG. 9B for thequantity r₀/r_(x), each as function of λ_(0,A)−λ_(C) and λ_(0,B)−λ_(C).r₀ is the minimum measurable bend radius for the standard fiber designhaving three outer cores as shown in FIG. 3A.

The two plots of 9A and 9B are combined in FIG. 10 . FIG. 10 shows thehighest curvature (1/r_(x)) measurable with 7 fiber cores as function ofthe smallest radius r_(min) still measurable with four fiber cores(including the center core) of the fiber sensor 12′ for various sensordesigns expressed by Δ. r_(min) ranges from 2.6 nm to 5.9 mm and r_(x)ranges from 5.1 nm to infinity on the edges. It can be taken from FIGS.9A, 9B and 10 that there are “local” optimal designs which maximallyleverage the trade-off between r_(min) and r_(x). For example, the caseof Δ=0 nm represents an optimum since all curves with Δ≠0 nm give riseto larger or at best equal values for r_(min). For the case of Δ=0 nm itis possible to derive an expression for the minimum measurable bendradius as a function of the offset in scan wavelength range. To thisend, a relative scan wavelength range offset O_(f) is introduced withO_(f)=|2(λ_(0,A)−λ_(C))/Δλ|=|2(λ_(0,B)−λ_(c))/Δλ|, where Δλ representsthe full scan range, which is 16.7 nm in the present example. The gainfactor f=r_(min)/r₀ is given by:

$\begin{matrix}{{f = {{\frac{1}{2}\frac{\sqrt{3}}{1 + O_{f}}{while}0} \leq O_{f} \leq \frac{\sqrt{3} - 1}{\sqrt{3} + 1}}}{f = {{\frac{1}{2}\frac{1}{1 - O_{f}}{while}\frac{\sqrt{3} - 1}{\sqrt{3} + 1}} \leq O_{f} \leq \frac{1}{3}}}{f = {{\frac{1}{1 + O_{f}}{while}\frac{1}{3}} \leq O_{f} \leq 1}}{\frac{r_{0}}{r_{x}} = {{1 - {O_{f}{while}0}} \leq O_{f} \leq 1}}} & (5)\end{matrix}$

From equation (5) and FIG. 10 it is clear that there is an optimum atO_(f)=(√{square root over (3)}−1)/(√{square root over (3)}+1) so thatf=0.68 and r₀/r_(x)=0.73. For a scan range of 16.7 nm and r₀, =5.1 mmthis constitutes a design with r_(min)=3.5 mm and r_(x)=7.0 mm (which isexactly the example as given in FIG. 8A). For a slightly smallerr_(min), r_(x) becomes directly much larger. This local optimum isachieved for λ_(0,A)−λ_(C)=2.3 nm. Similar considerations can be madefor other shape sensing fiber designs.

The above-described aspects are all valid in case of redundancy, i.e.the number of fiber cores in the fiber sensor is larger than the numberof quantities needed to accurately sense the shape of the optical fibersensor 12′. However, it can be advantageous to use the same aspects alsoin cases when even though strictly speaking there is no overallredundancy. It might be acceptable to lose information on less importantquantities in order to create temporarily or spatially “redundancy” foressential quantities required for shape sensing. For example, for somemeasurements or at some particular locations, e.g. with short bendshaving a smaller radius of curvature, only the signals of some of thefiber cores might be used so that that smaller bend radius still can beprobed. This might compromise accuracy a little, or this could becompensated with (temporal or spatial) interpolation or extrapolation ofsignals. This will be explained in more detail below.

With again reference to FIG. 6A, showing an optical fiber sensor 12′with 7-cores in total, wherein three temperature sensitive fiber coreshave different resonance wavelengths λ₀ in an unstrained statetherefore, axial strain, temperature, bend strain in two orthogonaldirections and twist strain can be measured, because the number ofquantities to be measured (five) is smaller than the number of fibercores (seven). The smallest radius of curvature for which theafore-mentioned quantities can be measured is 10.6 mm (r_(x)). Belowthis radius and above r_(min)=3.2 mm, only three outer fiber cores arestill in the spectrum. With these three outer fiber cores and the centerfiber core, still bend strain in two orthogonal directions and twiststrain can be measured, as well as the sum of the effects of axialstrain and temperature. Because axial strain and temperature cannot beseparated anymore, the accuracy of the other signals is compromised, butfor a small distance the remaining accuracy may still be sufficient.There may be many applications where the probability of tight bendsbeing present in the optical fiber sensor 12′ is low and, if they occur,the length of the tight bend is short and might even be at the end ofthe shape, for example in medical devices, reducing the effect on totalshape accuracy even more. As said before, the temperature and axialstrain separation at the places where 7 fiber cores are still availablemay be inter- or extrapolated to compensate for the loss in accuracy.Or, in other situations, the temperature and axial strain separation fora measurement with r_(min)<r<r, may be inter- or extrapolated frommeasurements that are close in time to the measurement with r>r_(x).

The above aspects which are suitable to reduce the minimum measurablebend radius using one or more of the embodiments of the optical fibersensor 12′ described above can be used in an optical shape sensingmethod. In the method, the optical fiber sensor (12′) is provided. Thefiber cores (1, 3, 5) of the first subset of fiber cores and the fibercores (2, 4, 6) of the second subset of fiber cores are interrogatedwith light. Reflection spectra of light returning from the fiber cores(1, 3, 5) of the first subset of fiber cores and the at least one fibercore (2, 4, 6) of the second subset of fiber cores are measured, and theshape of the optical fiber sensor (12′) based on the reflection spectrais reconstructed. The method can be performed with the system 10 in FIG.1 , wherein, as mentioned above, the system 10 has a correspondingnumber of optical channels 24 a-24 d which is larger than four. Thefiber sensors 12′ described above may be comprised by a medical device,like a catheter or guidewire.

While the invention has been illustrated and described in detail in thedrawings and foregoing description, such illustration and descriptionare to be considered illustrative or exemplary and not restrictive; theinvention is not limited to the disclosed embodiments. Other variationsto the disclosed embodiments can be understood and effected by thoseskilled in the art in practicing the claimed invention, from a study ofthe drawings, the disclosure, and the appended claims.

In the claims, the word “comprising” does not exclude other elements orsteps, and the indefinite article “a” or “an” does not exclude aplurality. A single element or other unit may fulfill the functions ofseveral items recited in the claims. The mere fact that certain measuresare recited in mutually different dependent claims does not indicatethat a combination of these measures cannot be used to advantage.

Any reference signs in the claims should not be construed as limitingthe scope.

The invention claimed is:
 1. An optical shape sensing system, comprisingan optical fiber sensor comprising an optical fiber having embeddedtherein a number of at least four fiber cores arranged spaced apart froma longitudinal center axis of the optical fiber, the fiber cores eachhaving wavelength dependent reflective structures disposed thereon and aresonance wavelength in response to light introduced into the fibercores in an unstrained state thereof, an optical interrogation unitconfigured to interrogate the fiber cores with light in a scanwavelength range including the resonance wavelengths of the fiber coresin an unstrained state of the fiber cores, wherein the opticalinterrogation unit is configured to set the scan wavelength range suchthat a center wavelength of the scan wavelength range is decentered withrespect to the resonance wavelength of at least one of the fiber cores,wherein the number of fiber cores comprises a first subset of firstfiber cores each having a first resonance wavelength in response tolight introduced into the first fiber cores in an unstrained statethereof, and a second subset of at least one second fiber core eachhaving a second resonance wavelength in response to light introducedinto the at least one second fiber core in an unstrained state thereof,wherein the first resonance wavelength differs from the second resonancewavelength, and wherein the interrogation unit is configured to set thescan wavelength range such that the center wavelength is between thefirst and second resonance wavelengths.
 2. The optical shape sensingsystem of claim 1, wherein the optical interrogation unit is configuredto set the scan wavelength range such that the center wavelength of thescan wavelength range is decentered with respect to the resonancewavelengths of all fiber cores.
 3. The optical shape sensing system ofclaim 1, wherein the first resonance wavelength of each of the firstfiber cores are equal with respect to one another, and the interrogationunit is configured to set the scan wavelength range such that the centerwavelength is in the middle between the first and second resonancewavelengths.
 4. The optical shape sensing system of claim 1, wherein theinterrogation unit is configured to set the scan wavelength range suchthat the center wavelength is decentered with respect to the resonancewavelengths of the at least one fiber core by less than half the scanwavelength range.
 5. The optical shape sensing system of claim 1,wherein the fiber cores are distributed in azimuthal direction aroundthe center axis equidistantly with respect to one another.
 6. Theoptical shape sensing system of claim 1, wherein the fiber cores aredistributed in azimuthal direction around the center axisnon-equidistantly with respect to one another.
 7. The optical shapesensing system of claim 1, wherein the number of fiber cores spacedapart from the longitudinal center axis is 5, 6, or more.
 8. The opticalshape sensing system of claim 1, wherein the optical fiber furthercomprises a central fiber core arranged on the center axis of the fiber.9. The optical shape sensing system of claim 1, further comprising anevaluation unit configured to reconstruct the shape of the fiber sensorusing a reflection spectra.
 10. An optical shape sensing method,comprising, using an optical fiber sensor comprising an optical fiberhaving embedded therein a number of at least four fiber cores arrangedspaced apart from a longitudinal center axis of the optical fiber, thefiber cores each having wavelength dependent reflective structuresdisposed thereon and a resonance wavelength in response to lightintroduced into the fiber cores in an unstrained state thereof:interrogating the fiber cores with light in a scan wavelength rangeincluding the resonance wavelengths of the fiber cores in an unstrainedstate of the fiber cores, the interrogating comprising setting the scanwavelength range such that a center wavelength of the scan wavelengthrange is decentered with respect to the resonance wavelength of at leastone of the fiber cores, wherein the number of fiber cores comprises afirst subset of first fiber cores having a first resonance wavelength inresponse to light introduced into the first fiber cores in an unstrainedstate thereof, and a second subset of at least one second fiber corehaving a second resonance wavelength in response to light introducedinto the at least one second fiber core in an unstrained state thereof,wherein the first resonance wavelengths differ from the second resonancewavelength, and wherein the interrogation unit is configured to set thescan wavelength range such that the center wavelength is between thefirst and second resonance wavelengths.
 11. A computer readable mediumstoring instructions that, when executed by a computer, cause an opticalshape sensing system to carry out the steps of the method of claim 10.